The rate law for a chemical reaction gives us information about the rate of the reaction with respect to the concentrations of the reactants. In this case, we are given the reaction 2A B gives product and we need to determine the rate law for this reaction.



We are given the following experimental data:

- Doubling the initial concentration of both reactants increases the rate by a factor of 8
- Doubling the concentration of B alone doubles the rate



We can determine the rate law for the reaction by using the experimental data to find the orders of reaction with respect to each reactant.

From the first piece of experimental data, we can see that the rate is proportional to the concentration of both A and B raised to some power. Let's call the order of reaction with respect to A "x" and the order of reaction with respect to B "y". Then, we can write:

rate = k[A]^x[B]^y

When we double the concentration of both A and B, the rate increases by a factor of 8. This means that:

(2[A])^x(2[B])^y = 8[A]^x[B]^y

Simplifying this expression, we get:

2^x * 2^y = 8

2^(x+y) = 8

x + y = 3

From the second piece of experimental data, we can see that doubling the concentration of B alone doubles the rate. This means that:

(2[A])^x(2[B])^y = 2[A]^x[2B]^y

Simplifying this expression, we get:

2^y = 2

y = 1

Now that we know the order of reaction with respect to B, we can use the first piece of experimental data to find the order of reaction with respect to A. We know that:

x + y = 3

y = 1

So:

x = 2

Therefore, the rate law for the reaction 2A B gives product is:

rate = k[A]^2[B]



In conclusion, the rate law for the reaction 2A B gives product is rate = k[A]^2[B]. We determined this rate law by using the experimental data given to us and finding the orders of reaction with respect to each reactant.